Richie Foran's fourth minute opener was added to in the 36th minute by Billy McKay - his third goal in as many matches this season, with Inverness producing a comprehensive attacking display in the opening 45 minutes.
After the interval, however, Caley Thistle were forced to defend under some pressure from Motherwell, but limited them to few chances as they ran out deserved winners, much to the delight of manager Butcher.
He said: "It was a good first half performance, but I felt that overall it was a game of two halves.
"We knew that with the wind in the second half Motherwell with get it forward to John Sutton, while they have good pace in their team.
"They caused us problems, but we defended well and showed a lot of grit, resilience and steel.
"That's the new mantra at this club - stamina, steel and style."
Motherwell's loss was their second in succession and boss Stuart McCall was left to bemoan his side's poor start.
He said: "We talked before the game about settling into the match, but then we find ourselves a goal down after four minutes.
"I thought that the tempo of the first half just wasn't good enough, so there's a lot of work to do.
"The second half from us was better, but it had to be.
"I thought they had the most outstanding player on the pitch in Richie Foran. He defended set pieces in their box, he won tackles in the midfield and scored a goal.
"It was a really disappointing performance and result. We have to show a bit more than we did against Inverness."